Exercise 3 | Wiskunde op Tilburg University

Antwoord 1 correct

Correct

Antwoord 2 optie

$z(2\frac{1}{7},5)=4\frac{29}{49}\sqrt{5}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$z(0,0)=0$

Antwoord 3 correct

Fout

Antwoord 4 optie

None of the other answers is correct.

Antwoord 4 correct

Fout

Antwoord 1 optie

$z(3\frac{3}{7},2)=11\frac{37}{49}\sqrt{2}$

Antwoord 1 feedback

Correct:

$\dfrac{z'_x(x,y)}{z'_y(x,y)}=\dfrac{2xy^{\frac{1}{2}}}{\frac{1}{2}x^2y^{-\frac{1}{2}}}=\dfrac{4y}{x}=\dfrac{7}{3}$ gives

$x=\frac{12}{7}y$ . Plugging this into the restriction gives

$7\frac{12}{7}y+3y=30$ , which results in

$y=2$ with

$x=\frac{12}{7}\cdot 2=3\frac{3}{7}$ .

$z(3\frac{3}{7},2)=11\frac{37}{49}\sqrt{2}$ . We check the boundaries:

$z(0,10)=0$ and

$z(4\frac{2}{7},0)=0$ . Hence,

$z(3\frac{3}{7},2)=11\frac{37}{49}\sqrt{2}$ is the maximum.

Go on.

Antwoord 2 feedback

Wrong:

$\dfrac{2}{\frac{1}{2}}\neq 1$ .

Try again.

Antwoord 3 feedback

Wrong:

$(x,y)=(0,0)$ does not satisfy the restriction.

See Constrained optimization functions of two variables.

Antwoord 4 feedback

Wrong: The correct answer is among them.

Try again.